Do Horn and Silk ever confess to their sins?
I'm not sure either Horn or Silk fully confess to their sins.
Silk is supposedly terribly upset that Horn sacrificed himself so he could live. This ostensibly is why he remained hiding for so long. He couldn't face Horn's twins over having done so. What he never confesses to, however, is that he gaslit Horn into believing that sacrifice of himself so that Silk may live, was the only way to prove he actually loved Silk. Silk had in a sense already prepared Horn's mind... by gaslighting him in this way, that if ever in future he needed someone to suffer death or distress FOR him, Horn would step up and do so -- he'd be like a sergeant Sand, so happy to have his head blown to pieces if it means the revival of Father Pas. It's in the text for us to understand this, but it's done so that you can mostly avoid doing so if you wish. Silk also never confesses that he deliberately wound the already angry Blood up, so that he would mostly certainly attempt an assignation attempt on his mother, Rose. He never admits that he prepared for the assassination of Rose, the woman he admired he feared more than any person in the whorl, to be done in a way that looked like an innocent mistake. However, he does subtly leave clues for us to conclude that he did so. He admits he knew Rose had named Blood "Blood" in order to make him feel unworthy of being nurtured by a mother. He knew Blood had a mother who deliberately abandoned her son in order to have some chance of regaining the love of the mother-god, Echidna, who'd abandoned her as soon as she took attention off of her onto her new born, and who showed she repudiated her son by naming him a (blood)stain, in that he shows that he knows that Nettle's mother named her "Nettle" to antagonize and repudiate her. Silk shows that he knows that antagonizing someone who's already upset is an effective way to have a crime committed but to be able to pretend innocence, in that he admits that he antagonized Jugano while on the Red Whorl, forcing his permanent removal from some "mother" he had met and bonded with in a cell, so that he would surely try and kill him when they got back. This was his means of committing suicide, but without others thinking he was culpable. It is for us however to look back and conclude that his antagonizing of Blood... via, as we remember, his withholding any quid pro quo after Blood had surrendered to him, into nearly murdering someone he had full right to hate already, a person so obnoxious, she, after abandoning him as a child, had just decided he had no right to resist her effort to assume a mother's presumed ownership of him in her calling him "Bloody" rather than "Blood," and who was tut-tutting him, in scolding mother fashion, was indeed a deliberate attempt to push him over the edge. It's there, but it requires a recovery, Silk might assume most people wouldn't want to make, because they, like Horn, have been conned into too much needing him as some kind of saviour figure.
Horn confesses to many things, but he writes his text so that many of his crimes against his wife are "innocent" ones. He dates Seawrack, a woman much younger and much more beautiful than Nettle, but he says she was basically forced on him by a dangerous Mother diety. What was he do to, leave her alone? he writes. He has many young wives and many children in Gaon, but this too was forced on him. He never in the text says that even if this was all forced on him, which they were, he nevertheless would have chosen to have these young wives, to have so many new children. That would have been an act of good faith, as it's clearly what he wanted. He admits he raped Seawrack, nearly to death, but this may have been compelled by Seawrack's son. What he never admits is that song or no song, for Seawrack admiring Krait's beauty and thus reminding him of his wife's abandonment of him for the more appealing Sinew, he would have raped her to death in any case. That would have been good faith, but he can't manage it. Horn never admits that he hated Nettle for switching attention off of him onto Sinew, and that the attack by Jahlee on Sinew, so soon after his birth -- the event that changed everything -- was more or less the near-murder that Horn was himself contemplating to inflict on Sinew. What he does instead is blame Sinew. He is guilty for stealing Nettle away from him. This again is bad faith. A displacement. And since he can never admit that he hated his wife, he can never consciously acknowledge that he brought the same inhuma who nearly killed Sinew as an infant, the same inhuma that delighted him so in nearly destroying the more-beautiful male Nettle had fallen in love with over him, back onto her at the finish for her to finish the job. It's there for readers to see. But most have chosen not to. This same event gets replayed elsewhere in Wolfe's works, and even more overtly.... but so far, still, readers refuse to do the job that the protagonists cannot do by themselves: show to all who they are, and the full darkness of their motivations.
You can't properly shrive characters like this, until all their crimes are out in the open. To their credit, they've given clues for some more perspicacious people than Remora, to ultimately perform.